Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Almost complex structure (1)
- Bochner Inequality (1)
- Camassa-Holm equation (1)
- Compression body graph (1)
- Cone (1)
-
- Curvature (1)
- De rham homotopy (1)
- Euler-Arnold equation (1)
- Generalized Harmonic (1)
- Geometric group theory (1)
- Geometric topology (1)
- Global weak solution (1)
- Graph (1)
- Heegaard splitting (1)
- Local well-posedness (1)
- Mapping class group (1)
- Poincar\'e Inequality (1)
- Positive drift (1)
- Quasi-geostrophic equation (1)
- Random walk (1)
- Rational homotopy theory (1)
- Right-angled Coxeter group (1)
- Sectional curvature (1)
- Six sphere (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez
Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez
Dissertations, Theses, and Capstone Projects
In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures …
Linear Progress With Exponential Decay In Weakly Hyperbolic Groups, Matthew H. Sunderland
Linear Progress With Exponential Decay In Weakly Hyperbolic Groups, Matthew H. Sunderland
Dissertations, Theses, and Capstone Projects
A random walk wn on a separable, geodesic hyperbolic metric space X converges to the boundary ∂X with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when (1) the step distribution has exponential tail and (2) the action on X is acylindrical. We extend exponential decay to the nonacylindrical case. We give an application to random Heegaard splittings.
Divergence Of Cat(0) Cube Complexes And Coxeter Groups, Ivan Levcovitz
Divergence Of Cat(0) Cube Complexes And Coxeter Groups, Ivan Levcovitz
Dissertations, Theses, and Capstone Projects
We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we characterize right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cubic. This generalizes a theorem of Dani-Thomas that addressed the class of 2-dimensional right-angled Coxeter groups. This characterization also has a direct application to the theory of random right-angled Coxeter groups. As another application of the divergence bounds obtained for cube complexes, we provide an inductive graph theoretic criterion on a right-angled Coxeter group's …
On Some Geometry Of Graphs, Zachary S. Mcguirk
On Some Geometry Of Graphs, Zachary S. Mcguirk
Dissertations, Theses, and Capstone Projects
In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size of …
Geometry And Analysis Of Some Euler-Arnold Equations, Jae Min Lee
Geometry And Analysis Of Some Euler-Arnold Equations, Jae Min Lee
Dissertations, Theses, and Capstone Projects
In 1966, Arnold showed that the Euler equation for an ideal fluid can arise as the geodesic flow on the group of volume preserving diffeomorphisms with respect to the right invariant kinetic energy metric. This geometric interpretation was rigorously established by Ebin and Marsden in 1970 using infinite dimensional Riemannian geometry and Sobolev space techniques. Many other nonlinear evolution PDEs in mathematical physics turned out to fit in this universal approach, and this opened a vast research on the geometry and analysis of the Euler-Arnold equations, i.e., geodesic equations on a Lie group endowed with one-sided invariant metrics. In this …